Most Irish records before the middle of the 19th. C were lost in a fire in Dublin during the Irish Civil War. What survives is mostly census substitutes. Some early church records have survived. It was a common custom to record family dates in family bibles and some of the McElderrys now living in the Ballymoney area may have such information. They could be traced through bt.com. A second source of information is the Public Record Office for Northern Ireland in Belfast who have McElderry information which can be found listed at:www.proni.gov.uk/index_alphabetical_index_to_private_deposit...
They have information on the family from 1690, letters from Leitrim 1795-98 and a map pertaining to Robert McElderry from the 1820's. The PRONI references are T 2414 and MIC57.
If you cannot visit PRONI you could pay a professional genealogist (many listed in the PRONI web site)to do the research for you. Incidentally there is a gravestone in Delgany, Co. Wicklow of Thomas Lyle McElderry, born in Ballymoney May 28, 1872 and died Aug. 23, 1956. His wife Kathleen d. Dec. 13, 1964. He likely was a Presbyterian minister as his home address was Old Rectory, Delgany.